Quantum computing quantum Monte Carlo with hybrid tensor network for electronic structure calculations

TL;DR

This paper introduces a hybrid tensor network approach to quantum Monte Carlo on quantum computers, enabling high-accuracy electronic structure calculations for larger systems beyond current device limitations.

Contribution

The paper proposes a novel algorithm combining QC-QMC with hybrid tensor networks, extending applicability to larger quantum systems and demonstrating noise robustness.

Findings

Achieves energy accuracy several orders of magnitude higher than traditional QMC.

Hybrid tensor network version matches QC-QMC accuracy with system decomposition.

Demonstrates noise robustness with near-same accuracy on real quantum devices.

Abstract

Quantum computers have a potential for solving quantum chemistry problems with higher accuracy than classical computers. Quantum computing quantum Monte Carlo (QC-QMC) is a QMC with a trial state prepared in quantum circuit, which is employed to obtain the ground state with higher accuracy than QMC alone. We propose an algorithm combining QC-QMC with a hybrid tensor network to extend the applicability of QC-QMC beyond a single quantum device size. In a two-layer quantum-quantum tree tensor, our algorithm for the larger trial wave function can be executed than preparable wave function in a device. Our algorithm is evaluated on the Heisenberg chain model, graphite-based Hubbard model, hydrogen plane model, and MonoArylBiImidazole using full configuration interaction QMC. Our algorithm can achieve energy accuracy (specifically, variance) several orders of magnitude higher than QMC, and the hybrid tensor version of QMC gives the same energy accuracy as QC-QMC when the system is appropriately decomposed. Moreover, we develop a pseudo-Hadamard test technique that enables efficient overlap calculations between a trial wave function and an orthonormal basis state. In a real device experiment by using the technique, we obtained almost the same accuracy as the statevector simulator, indicating the noise robustness of our algorithm. These results suggests that the present approach will pave the way to electronic structure calculation for large systems with high accuracy on current quantum devices.